Boateng endured a horrendous World Cup in Russian Federation this summer.
His performances in Russian Federation - and for Leicester in the Premier League after signing from Hull City in a £17m deal last summer - mean he has attracted interest from Jose Mourinho, who is believed to have made Maguire his top target ahead of the new season.
Boateng's proposed move to Paris Saint-Germain has stalled so Bayern are looking for a new buyer and it appears they've offered Manchester United the chance to sign the former Manchester City defender.
Yerry Mina seems to be the most possible option at the moment.
However, Rummenigge insists Bayern already have sufficient depth in the final third and don't need to add Martial to their ranks.
Harry Maguire Man Utd boss Jose Mourinho wanted Leicester defender
"Finally, it's over. Finally, such a hard pre-season is over", Mourinho told mufc.com.
First half: Manchester United vs Bayern Munich - the first half ended goalless.
Anthony Martial hit top form halfway through the previous season only to have his starting berth taken away by the new signing Alexis Sanchez. Chelsea wouldn't want to do it either after what happened with Nemanja Matic.
Who Mourinho deploys on the right of attack might well decide just how close they go to overhauling City this season.
They might not start off with the likes of Victor Lindelof and Marcus Rashford nailing down positions but Mourinho might ideally have them in the starting XI if they are playing at their best. "He always wanted it", Mourinho said of Rashford's switch from 19 to 10.
And Leicester are holding out a similar offer as United look to salvage a summer during which manager Jose Mourinho has complained over their lack of signings.